Strengthening Concepts 1. The ratio of broken to working piano keys was 2 to 9 . If there were (45) 88 keys on the old piano, how many were broken?

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1. Let the number of broken keys be $$ b $$ and the number of working keys be $$ w $$.
2. The ratio of broken to working keys is given as $$ 2:9 $$, so we have:
   $$
   \frac{b}{w} = \frac{2}{9}
   $$
3. The total number of keys is $$ 88 $$, hence:
   $$
   b + w = 88
   $$
4. Instead of solving the system directly, notice that the ratio $$ 2:9 $$ means the total is divided into $$ 2+9=11 $$ parts.
5. The number of keys corresponding to one part is:
   $$
   \text{One part} = \frac{88}{11} = 8
   $$
6. Thus, the number of broken keys (which correspond to 2 parts) is:
   $$
   b = 2 \times 8 = 16
   $$

Therefore, the number of broken keys is $$ 16 $$.
There were 16 broken keys.

Strengthening Concepts 1. The ratio of broken to working piano keys was 2 to 9 . If there were (45) 88 keys on the old piano, how many were broken?

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